I am a beginner in music theory and trying to understand some basic concepts.

As far as I understood, songs are played in keys. This essentially means that you pick a scale (let's say, C major) and you use notes of that scale. Chords can be built from notes that are in the key of C major. Notes of the C, G, Am and F chords for instance are all from the C major scale, thus a progression C-G-Am-F is also in the key of C major.

Now, when it comes to improvising, one can play the C major scale over the entire progression. One can, however, also choose to play different scales over the different chords: G major (among others) could be played over the G chord, for instance. This scale, however, contains an F#. Does this mean that playing a G major scale over the G chord in the above progression moves part of the song out of the key of C major? If so, how can I possibly establish the key of a particular song? If a song has as many keys as chords, the concept of key looses any meaning.

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Better to write a progression in roman numerals as I V vi IV. a progression is usually within a single key. If you move to the key of G, then its I V vi IV are a different set of chords than in the key of C. If you play the scale of G over your first progression it will clash when you get to the F chord. Also to establish a new key (modulate) you'd probably want to play multiple chords within that new key to really establish a new tonal center.
– foreyezFeb 11 at 22:35

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Where does the linked question provide a direct answer to this question? (I wouldn't be surprised if there is already an answer to this somewhere on the site, but I couldn't immediately see that the linked question represents one....)
– topo mortoFeb 11 at 23:00

@topomorto I agree, it's not immediate. But the accepted answer there is a reasonable summary. I prefer, however, the direct answers provided here.
– BotondFeb 11 at 23:04

3 Answers
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Keys are one way of making sense of the harmony of a piece of music. They're a very common way, and often a useful way, but not always. Don't make the mistake of thinking that keys are absolutely fundamental to the way music works - they're simply one way of looking at things.

This essentially means that you pick a scale (let's say, C major) and you use notes of that scale. Chords can be built from notes that are in the key of C major. Notes of the C, G, Am and F chords for instance are all from the C major scale, thus a progression C-G-Am-F is also in the key of C major.

That's a good description of what would be a very simple 'beginner' way of creating harmony using the major/minor system. But of course, you're allowed to go outside of the notes in one key, and you're allowed to go outside the chords in one key...

. One can, however, also choose to play different scales over the different chords: G major (among others) could be played over the G chord, for instance. This scale, however, contains an F#. Does this mean that playing a G major scale over the G chord in the above progression moves part of the song out of the key of C major?

...which as you say, raises the interesting question - if you're going outside of the notes in one key, at what point does that mean that you're in a different key?

Ultimately, there aren't really any strict rules you can make. One person might consider a certain chord progression or melodic sequence of notes to constitute a key change; another might think that it's a borrowed chord, or feel that the piece was in a different key to begin with.

How can I possibly establish the key of a particular song?

Well, if there's officially-published sheet music that shows the key, then that's the key. Even then, you might want to argue that the way it has been notated isn't the best.

If a song has as many keys as chords, the concept of key looses any meaning.

Not really, because as I said at the start, a key isn't a fundamental part of the nature of a piece of music - it's simply a perspective from which you can look at the harmony. Sometimes it might be interesting and valuable to look at a part of a chord progression both from the perspective of considering that there has been a chord change, and from the perspective of considering that there hasn't.

The most important aspect of a key is not the pitch collection, but its tonal center, the home base note. It's not the notes, it's what you do with them. (I did not say that the pitch collection does not matter at all.)

If you play a long sequence of notes from the C major scale completely randomly and without emphasizing any of them dynamically or with timing differences - or if you play them with completely random emphasis, then your "song" is not in C major, it's probably not in any key at all, it's just random rubbish.

Play these notes in this order: C, C, D, E, F, F, F.

Does it feel like F is the home base?

Then play these notes in this order: G, F, E, D, C, C, C.

Does it now feel like C is the home base?

To establish the C major key, a quick and easy way is to play a chord cadence like C major, F major, G major, C major. But so the final C major feels like you at least briefly stopped there. Dynamics and timing are a big part of how a tonal center is established.

Merely using notes from outside of the key is not necessarily enough to change the key of a piece of music. Playing in a certain key has less to do with the particular collection of notes which are used, and more to do with how those notes function.

If you're playing in the key of C, this means that the note C (and its associated chord) function as the tonal center or "tonic"; it's the chord which feels the most stable and "at rest", so to speak. You can think of C as "home base" and all other chords as either pulling away from, or leading back towards it (this is of course a simplified explanation, if you really want to dig into this you should look into something called functional harmony).

Once this sense of tonal center is established, using a few non-scale tones (or even entire chords) is generally not enough to disrupt our sense of which chord is the tonic. Such "outside" notes are instead used to add variation or color to the music; in fact non-scale notes are often called "chromatic notes", which comes from the greek word for color: "chroma".

Now, if you wanted to actually change the key of a song, there are of course ways of doing that - it's called modulation, and there are many ways of going about it.

Finally, it should be noted that different genres and styles of music have different ways of approaching these things, and that it's often a manner of preference as to how you chose to describe things. When it comes to these theoretical question it's often possible to analyze things in different ways, without any particular answer necessarily being more "correct". Some pieces of music seem to make more sense if we think of them as changing keys a lot, while others are more reasonably understood in terms of a single key. It really needs to be done on a case-by-case basis a lot of the time.